LA MATEMATICA BORROSA Y EL PRECIO DE EQUILIBRIO: UNA APLICACIÓN A LAS AGUAS DEPURADAS

Ante la necesidad de conocer el valor de los bienes carentes de mercado, nuestro objetivo a lo largo del presente artículo es la propuesta de un mecanismo para su determinación. Partiendo del método de valoración contingente (CVM) utilizado en un entorno crisp, se aporta una metodología para agregar las opiniones inciertas con el objeto de obtener el precio de equilibrio. Un análisis posterior permitirá analizar la conveniencia de fijar subvenciones o impuestos sobre los mismos. La inexistencia de observaciones pasadas nos lleva a utilizar instrumentos de la teoría de los Fuzzy Sets. Para ello se seleccionarán dos grupos de expertos, unos que representarán a los demandantes y otro a los oferentes. Mediante sucesivas fases de petición de opinión y de suministro de información se determinarán ambos precios, y su intersección permitirá obtener el precio de equilibrio, de acuerdo con la teoría clásica. A lo largo del trabajo se han establecido criterios para determinar el número máximo de las mismas, teniendo presente la dispersión de las opiniones y su variación en dos fases consecutivas. En último lugar se realiza una aplicación del mismo para la determinación del precio de equilibrio del agua depurada en la provincia de Alicante (España). Para ello se ha realizado una encuesta a las empresas depuradoras de aguas residuales (EDAR) como oferentes y a los agricultores y empresas distribuidoras de aguas como demandantes. Palabras clave: función de demanda, función de oferta, precio de equilibrio, elasticidad, distancia borrosa, EDAR, agua depurada. Abstract Giving the necessity to know the price of a non-marketed good, our objective throughout the present paper is the proposal of a mechanism for their determination. Starting from the contingent valuation method (CVM) used in a crisp environment; we will propose a methodology to aggregate fuzzy opinions in order to get the equilibrium price. Further analysis will allow us to evaluate the convenience of fixing subsidies or taxes on such non-marketed goods. Previous works have deal with fuzzy demand and supply functions (Yager, 2000; Dompere, 1997). This paper will focus on the process of requesting supplying information. Two groups of experts were selected, one representing demand and the other supply. After successive phases, both prices were determined, and their intersection made it possible to obtain the market price in accordance with classical theory. The study established criteria for determining the maximum number of phases, bearing in mind the dispersion of opinions and their variation in two consecutive phases. Finally, the mechanism was applied to determine the market price of treated wastewater in the province of Alicante (Spain). A survey was made to the wastewater treatment plants (WWTP) as suppliers and farmers and water distribution companies as consumers. Keywords: demand function, supply function, equilibrium price, elasticity, fuzzy distance, WWTP, treated water

Seismic Risk Management

Seismic risk management is a problem of many dimensions, involving multiple inputs, interactions within risk factors, criteria, alternatives and stakeholders. The deployment of this process is inherently fraught with the issues of complexity, ambiguity and uncertainty, posing extra challenges in the assessment, modelling and management stages. The complexity of earthquake impacts and the uncertain nature of information necessitate the establishment of a systematic approach to address the risk of many effects of seismic events in a reliable and realistic way. To fulfill this need, the study applies a systematic approach to the assessment and management of seismic risk and uses an integrated risk structure. The fuzzy set theory was used as a formal mathematical basis to handle uncertainties involved within risk parameters. Throughout the process, the potential impacts of an earthquake as the basic criteria for risk assessment were identified and relations between them were accommodated through a hierarchical structure. The various impacts of an earthquake are then aggregated through a composite fuzzy seismic risk index (FSRi) to screen and prioritize the retrofitting of a group of school buildings in Iran. Given the imprecise data which is the prime challenge for development of any risk model, the proposed model demonstrates a more reliable and robust methodology to handle vague and imprecise information. The significant feature of the model is its transparency and flexibility in aggregating, tracing and monitoring the risk impacts. The novelty of this study is that it serves as the first attempt of the process of a knowledge base risk-informed system for ranking and screening the retrofitting group of school buildings. The model is capable of integrating various forms of knowledge (quantitative and qualitative information) extracted from different sources (facts, algorithms, standards and experience). The outcomes of the research collectively demonstrate that the proposed system supports seismic risk management processes effectively and efficiently

Neutrosophic SuperHyperAlgebra and New Types of Topologies

In general, a system S (that may be a company, association, institution, society, country, etc.) is formed by sub-systems Si { or P(S), the powerset of S }, and each sub-system Si is formed by sub-sub-systems Sij { or P(P(S)) = P2(S) } and so on. That’s why the n-th PowerSet of a Set S { defined recursively and denoted by Pn(S) = P(Pn-1(S) } was introduced, to better describes the organization of people, beings, objects etc. in our real world. The n-th PowerSet was used in defining the SuperHyperOperation, SuperHyperAxiom, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyperAxiom in order to build the SuperHyperAlgebra and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one in fact encounters SuperHyperStructures. Also, six new types of topologies have been introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology

A practical development of multi-attribute decision making using fuzzy set theory

The foundations of multi-attribute utility theory are reviewed and compared with the author's practical experience and other psychological studies of decision-making. The case is presented for a new approach to decision-making, moving away from the strictly numerical techniques. Instead of concentrating on the normative or descriptive aspects of decision-making, themed-problem of decision-making is studied, thereby giving the decision-maker more control over the decision-making process and ensuring a more truly participative approach to design and decision-making. The problem of uncertainty is also tackled by considering it from both the stochastic and fuzzy standpoints. A revised approach to the assessment of uncertainty and its incorporation in the decision-making process is advocated. The theoretical framework behind these ideas is expressed using fuzzy set theory. Previous attempts to apply fuzzy set theory to multi-attribute decision-making are reviewed and criticised for their failure to tackle the basic assumptions of multi-attribute utility theory. A practical methodology for using verbal descriptions is derived, and illustrated with a worked example. A practical description of how to apply the method is included, and the results of some applications are presented

Prioritisation of requests, bugs and enhancements pertaining to apps for remedial actions. Towards solving the problem of which app concerns to address initially for app developers

Useful app reviews contain information related to the bugs reported by the app’s end-users along with the requests or enhancements (i.e., suggestions for improvement) pertaining to the app. App developers expend exhaustive manual efforts towards the identification of numerous useful reviews from a vast pool of reviews and converting such useful reviews into actionable knowledge by means of prioritisation. By doing so, app developers can resolve the critical bugs and simultaneously address the prominent requests or enhancements in short intervals of apps’ maintenance and evolution cycles. That said, the manual efforts towards the identification and prioritisation of useful reviews have limitations. The most common limitations are: high cognitive load required to perform manual analysis, lack of scalability associated with limited human resources to process voluminous reviews, extensive time requirements and error-proneness related to the manual efforts. While prior work from the app domain have proposed prioritisation approaches to convert reviews pertaining to an app into actionable knowledge, these studies have limitations and lack benchmarking of the prioritisation performance. Thus, the problem to prioritise numerous useful reviews still persists. In this study, initially, we conducted a systematic mapping study of the requirements prioritisation domain to explore the knowledge on prioritisation that exists and seek inspiration from the eminent empirical studies to solve the problem related to the prioritisation of numerous useful reviews. Findings of the systematic mapping study inspired us to develop automated approaches for filtering useful reviews, and then to facilitate their subsequent prioritisation. To filter useful reviews, this work developed six variants of the Multinomial Naïve Bayes method. Next, to prioritise the order in which useful reviews should be addressed, we proposed a group-based prioritisation method which initially classified the useful reviews into specific groups using an automatically generated taxonomy, and later prioritised these reviews using a multi-criteria heuristic function. Subsequently, we developed an individual prioritisation method that directly prioritised the useful reviews after filtering using the same multi-criteria heuristic function. Some of the findings of the conducted systematic mapping study not only provided the necessary inspiration towards the development of automated filtering and prioritisation approaches but also revealed crucial dimensions such as accuracy and time that could be utilised to benchmark the performance of a prioritisation method. With regards to the proposed automated filtering approach, we observed that the performance of the Multinomial Naïve Bayes variants varied based on their algorithmic structure and the nature of labelled reviews (i.e., balanced or imbalanced) that were made available for training purposes. The outcome related to the automated taxonomy generation approach for classifying useful review into specific groups showed a substantial match with the manual taxonomy generated from domain knowledge. Finally, we validated the performance of the group-based prioritisation and individual prioritisation methods, where we found that the performance of the individual prioritisation method was superior to that of the group-based prioritisation method when outcomes were assessed for the accuracy and time dimensions. In addition, we performed a full-scale evaluation of the individual prioritisation method which showed promising results. Given the outcomes, it is anticipated that our individual prioritisation method could assist app developers in filtering and prioritising numerous useful reviews to support app maintenance and evolution cycles. Beyond app reviews, the utility of our proposed prioritisation solution can be evaluated on software repositories tracking bugs and requests such as Jira, GitHub and so on

Using Yager's t-norms for aggregation of fuzzy intervals

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel W 50 (139) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman